Functional analysis within latent states: A novel framework for analysing functional time series data

Functional data analysis (FDA) enables modelling and interpretation of data represented as functions over a continuum like time, space, or frequency. This paper introduces the flawless analysis framework (FunctionaL Analysis Within LatEnt StateS), a nested FDA framework for analysing functional time series data. It provides comprehensive insights into the interplay between latent state characteristics, state occupancy dynamics, and functional attributes within states, while maintaining interpretability at each level. Applying flawless to functional time series of power spectral densities from electroencephalography (EEG) data from the Healthy Brain Network, we explore functional characteristics of resting state brain activity in n = 503 early adolescents aged 9 - 15 (X¯=11.5, SD = 1.7). We identify four functional latent states associated with variations in psychopathology and cognitive function. Bayesian regression models reveal important associations between the dynamics of latent state occupancy, functional traits within states, and relevant health measures. The integration of multiple FDA tools offers rich insights into functional and time-frequency characteristics of longitudinal data. For neuroscientific data this requires fewer assumptions about oscillatory peak frequencies, and captures more detailed frequency domain characteristics. flawless offers utility for novel and sophisticated insights into functional time series data across a range of areas for research and practice.